Chris Pine spends most of "The Finest Hours" stuck in a motor lifeboat being pumme|Claire Folger

“The Finest Hours” is a mixed bag — a movie so at war with itself that its split personality is reflected in its poster. Underneath an image of a behemoth of a ship trying to stay afloat amidst torrential super-weather run the words “based on the incredible true story.” So far, par for course for a live-action Disney film, which tend to exclusively peddle real-life triumphs of the human spirit. Up top, though, reads a far grimmer, more fatalistic, less human spirit triumphing proclamation: “We all live or we all die.”

“The Finest Hours” is both extremes. It tells of the storied, improbable rescue of two oil tankers caught up in a wicket nor’easter off of Cape Cod — a broadly drawn tale of underdogs fighting against the odds and coming out on top. It has a corny prologue, people screeching things like “Jesus, Mary and Joseph!” and “Not on my watch!”, plus a sadsack hero — a lowly Coast Guard runt played by Chris Pine — we know is weak because his fiancee, Miriam (Holliday Grainger), proposed to him, not the other way around. It’s why Pine’s Bernard lights out on a suicide rescue mission in the first place: Appropriately emasculated by his ball-busting colleagues, he has to man up.

On the other hand, Miriam is portrayed as headstrong, and the screenplay doesn't forget about her even when it's delivering its main attraction: manly men being pummeled inside a wave pool studio.The crews of both tankers, who’ve converged onto one, aren’t sure anyone’s coming. What follows is a tough look at the process of staying alive via problem solving, a la “Apollo 13” and “The Martian.” It even goes light on sentimentality and weepy moments. After all, its characters are too busy with the gruntwork of survival to worry about whether viewers are getting much in the way of feels.

Scenes of crazy plans being hatched and enacted are the best parts of “The Finest Hours,” in part because it gives us Casey Affleck. A technician and resident cucumber cool braniac, his Ray is not just the crews’ savior but is played by the only performer doing anything interesting. It’s like he’s been airlifted in from a movie where everyone’s a Method actor. Introspective and prone to mumbling, the still superior Affleck slips unpredictable moments into a film that should be, and sometimes is, simple. He lets out a gallows humor laugh when announcing the ship is definitely sinking, and cracks a big grin when someone grumbles about a plan that will either save or kill everybody.

Affleck’s detachment sometimes feels like mere apathy, but he helps occasionally ground a movie that’s all over the place. Director Craig Gillespie isn’t a maximalist — his credits include “Lars and the Real Girl” and “Million Dollar Arm” — and especially isn’t one who should be dealing with giant ships at sea. One shot of rain beating down on various sized boats is like any other, even with the occasional “money shot” writ in 3-D that makes everything look artificial. The scenes on the tankers that don’t feature Affleck feel broad: there’s a burly chef who sings from the “Guys and Dolls” songbook, plus a token mutinous bad egg who’s wrong about everything.

But sometimes it’s right on. It underplays the scenes with Grainger’s Miriam, even ones where she repeatedly begs her fiance’s no-nonsense boss (Eric Bana, perennially underused as a bland official type) to order the lifeboat back to shore. Instead of building with strings as she Erin Brockoviches through righteous anger, the scene plays out plainly, with Grainger repeating the same plea with the same deceptively flat inflection. Then again, it can’t even make the basic details of its story clear. Time and again characters struggle to do something unlikely, then it works out. Gillespie never even adequately shows the space of the small lifeboat, so we may not even understand how a large crew could ever fit without it sinking to the ocean floor. Then again, one thing it doesn’t tend to look or feel like is a Disney movie.